The Bayes theorem is:

$P(\theta | x)=\displaystyle \frac{p(\theta)L_x(\theta)}{\int_{\theta \in A}p(\theta)L_x(\theta)d\theta}$

It's pretty clear that $\theta's$ support will not change as bayes theorem update its distribution given some data, if $\theta's$ support is $(a,b)$ so it's easy to define a uninformative prior ( I'd just use $U(a,b)$) but when the support is either:

  • $A=(-\infty,\infty)$
  • $A=(0,\infty)$
  • $A=(-\infty,0)$

it becomes trouble to get a non-informative prior like $U(a,b)$ so Is there any alternative for a uninformative prior distribution to get through this?

  • 4
    $\begingroup$ Why do you need an uninformative prior? Such a thing doesn’t really exist.. If you really need, why not just using an improper “flat” prior? $\endgroup$
    – Tim
    Oct 14, 2021 at 22:23
  • $\begingroup$ There is almost no prior information where I work.I've never been told about what flat prior is. $\endgroup$ Oct 14, 2021 at 22:46